Geodesic
Three loops calculation of the field anomalous dimension in the full four-fermion
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 359-371 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a three-loop calculation for the contribution of the anomalous dimension $\gamma\psi$ in the RG function for the full $U_N$-symmetric model using dimensional regularization with $d=2+\varepsilon$. This model contains an infinite number of independent four-fermion interactions and couplings $g_n$. In the MS scheme, the three-loop contribution in $\gamma\psi$ depends on all of the charges. In the symmetric subtraction scheme for $\varepsilon=0$, only the dependence on the three lower charges $g'_{0,1,2}$ remains. The results of a three-loop calculation of $\gamma\psi$ for the Thirring model and for the Gross–Neveu model are discussed; they seem to contradict the equivalence of all four-fermion interactions for $d=2$, $N=1$. It is shown that this equivalence appears only for the symmetric subtraction scheme. The precise meaning of $(2+\varepsilon)$-expansions of the critical dimensions is discussed for when the multiplication renormalizability is absent in the Gross–Neveu model. 
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     title = {Three loops calculation of the field anomalous dimension in the full four-fermion},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {359--371},
     year = {1996},
     volume = {107},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a1/}
}
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A. N. Vasil'ev; M. I. Vyazovskii; S. È. Derkachev; N. A. Kivel'. Three loops calculation of the field anomalous dimension in the full four-fermion. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 359-371. http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a1/

[1] A. Bondi, G. Curci, G. Paffuti, P. Rossi, Ann. Phys., 199:3 (1990), 268 | DOI | MR

[2] A. N. Vasilev, M. I. Vyazovskii, S. E. Derkachev, N. A. Kivel, TMF, 107:1 (1996), 27–46 | DOI | MR | Zbl

[3] J. A. Gracey, Nucl. Phys., B341 (1990), 403 | DOI

[4] K. Furuya, R. E. Gamboa, Saravi, F. A. Schaposnik, Nucl. Phys., B208 (1982), 159 | DOI | MR

[5] D. J. Gross, A. Neveu, Phys. Rev., D10 (1974), 3235

[6] C. Luperini, P. Rossi, Ann. Phys., 212 (1991), 371 | DOI | MR

[7] J. A. Gracey, Nucl. Phys., B367 (1991), 657 | DOI | MR

[8] J. Zinn-Justin, Nucl. Phys., B367 (1991), 657 | MR

[9] A. N. Vasilev, S. E. Derkachev, N. A. Kivel, A. S. Stepanenko, TMF, 92:3 (1992), 486 | MR

[10] J. A. Gracey, Int. J. Mod. Phys., A9 (1994), 727 | DOI

[11] A. N. Vasilev, A. S. Stepanenko, TMF, 97:3 (1993), 364 | MR

[12] J. A. Gracey, Int. J. Mod. Phys., A6 (1991), 395 | DOI

[13] J. A. Gracey, Int. J. Mod. Phys., A9 (1994), 567 | DOI

[14] N. A. Kivel, A. S. Stepanenko, A. N. Vasiliev, Nucl. Phys., B367 (1991), 657